Question

What is the distance to the earth’s horizon from point P? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

Answer 1

Answer:

156.7 miles

Step-by-step explanation:

Since $x$ is tangent to the circle, then it is also a right angle with the radius, from here, just do Pythagorean theorem ($a^{2}+b^{2}=c^{2}$) to solve for $x$.

Since 1 leg and the hypotenuse is given to you, you want to solve for the other leg, which is $x$ (either $a$ or $b$). Lets use $b$ for $x$ and set up the equation.

$b^{2}=c^2-a^2$

$b^2=(3959+3.1)^2-3959^2$

$b^2 = 3962.1^2 - 3959^2$

$b^2 = 15,698,236.41 - 15,673,681$

$b^2 = 24,555.41$

$\sqrt{b^2}=\sqrt{24,555.41}$

$b=156.7016592$

$b=156.7$ (round to nearest tenth)

Answer 2

Answer: 156.7

Step-by-step explanation: Just confirming the answer :)